Sure, as others says, changing the the approach could be a better way to work with EF and DB, but starting from the fact you need Database First, I think working with Database First Model has it's advantages, one of those (and from this depends the answer to your second question) is the EDMX is taken as is, this implies as a generated piece of code, you can refresh, destroy and recreate that every time you need or want without loosing any modification.
Now, as I said before, the nature of generated code, implies every change you made to the EDMX will be lost, so sure you can remove a property, but the model and db are not transparently in sync.
I think the best way to do that is
- Update the database structure
- Update the EDMX, if the update "fails", meaning the changes are not reflected, destroy EDMX and then recreate it
Even if this way could be a simplistic approach, doesn’t cheating the nature of database first.
Just a note: working with database first, could be assisted by using partial classes to add things to the DbContext and entities involved to add functionalities and behaviours..